10. Roots and Zeros
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Construct a table to find all of the possible values of the expression for each of the values from the replacement set.
± 1, ± 2, ± 4, ± 8, ± 1/5, ± 2/5, ± 4/5, ± 8/5
To find all of the possible values of ± ba, replace both variables with each value from the replacement sets and simplify the expression.
| ± | a | b | ±b/a | Simplify |
|---|---|---|---|---|
| + | 1 | 1 | +1/1 | 1 |
| - | 1 | 1 | -1/1 | -1 |
| + | 1 | 2 | +2/1 | 2 |
| - | 1 | 2 | -2/1 | -2 |
| + | 1 | 4 | +4/1 | 4 |
| - | 1 | 4 | -4/1 | -4 |
| + | 1 | 8 | +8/1 | 8 |
| - | 1 | 8 | -8/1 | -8 |
| + | 5 | 1 | +1/5 | 1/5 |
| - | 5 | 1 | -1/5 | -1/5 |
| + | 5 | 2 | +2/5 | 2/5 |
| - | 5 | 2 | -2/5 | -2/5 |
| + | 5 | 4 | +4/5 | 4/5 |
| - | 5 | 4 | -4/5 | -4/5 |
| + | 5 | 8 | +8/5 | 8/5 |
| - | 5 | 8 | -8/5 | -8/5 |
We can now write all of the possible values of ± ba. ± 1, ± 2, ± 4, ± 8, ± 1/5, ± 2/5, ± 4/5, ± 8/5